Problem: Solve for $x$ : $4x^2 + 44x + 40 = 0$
Explanation: Dividing both sides by $4$ gives: $ x^2 + {11}x + {10} = 0 $ The coefficient on the $x$ term is $11$ and the constant term is $10$ , so we need to find two numbers that add up to $11$ and multiply to $10$ The two numbers $1$ and $10$ satisfy both conditions: $ {1} + {10} = {11} $ $ {1} \times {10} = {10} $ $(x + {1}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 1) (x + 10) = 0$ $x + 1 = 0$ or $x + 10 = 0$ Thus, $x = -1$ and $x = -10$ are the solutions.